And there were news reports at the time (there’s a scan of at least one relevant newspaper page on the wikipedia page)
Right, but there were no records of the event itself, just records of people’s testimonies. This is somewhat… odd. When e.g. a volcano erupts there is usually tons of footage of the actual event. People can be mistaken, or they can lie; but it’s hard to argue with a giant flaming mountain.
...being told that they had caught a Great White is still evidence in favour of a Great White having been caught.
Yes, but it’s also evidence for any number of other, more likely events: that my friends are pulling a prank, that they are mistaken, that a prank has been pulled on them, etc. etc. We don’t need to enumerate them all; what’s important here is only the posterior probability. If it is minute, then the reasonable course of action is to say, “until I see that shark, I won’t believe that you guys caught it, sorry”. There’s a huge difference between saying that, and saying, “even though the chances that you caught that shark are even smaller than the chances of a meteorite hitting me in the head anytime soon, I can’t come up with a better explanation off the top of my head so I’ll believe you, good job !”.
You said,
When I say that empirical evidence is rare, I mean that many things can be adequately explained whether it is true that God exists or not.
But beliefs do not exist in a vacuum. Instead, they form a Bayesian network: pieces of evidence affect the posterior probabilities of some beliefs; those beliefs change the prior probabilities of other beliefs, and so on. And the problem with the proposition G, which means “a god of some kind exists”, is that it’s starting to look like for any piece of evidence E, P(G|E) is lower than P(x|E), where x is pretty much any other non-divine explanation; and there is a lot of other evidence that can raise P(x). This is what I was driving at earlier with my hypothetical Alpha-god.
So, is there any piece of evidence E for which P(G|E) is much higher than any alternatives ? Moses, presumably, got exactly such a piece of evidence in the form of a burning bush. We don’t have that, however; what we’ve got is an ancient story about a guy who saw a burning bush, and experience tells us that ancient stories mostly can’t be trusted—or else we’d be forced to believe in Zeus, Shivah, the Jade Emperor, etc., possibly at the same time.
Rather than continue to talk in hypotheticals, I think I’ll take a moment to describe the incident in question (and I think you’ll see why I say I expect you to be unconvinced by it).
As you have anticipated, I am unconvinced by your report, but the question is, why are you convinced ? You say:
So, what makes me trust the evidence? I remember it; and I do not believe there was any way that any human could have faked that experience.
But these aren’t the only possibilities. Even if you cannot come up with any others (such as a random brain malfunction, as Jiro points out), why is this experience sufficient to convince you that a miracle occurred—given that, as you agreed above, the probability of such an event is minute ? Don’t you want to see the actual shark, before making your conclusions ?
Right, but there were no records of the event itself, just records of people’s testimonies. This is somewhat… odd. When e.g. a volcano erupts there is usually tons of footage of the actual event.
There appear to have been quite a few pictures—somewhat to my surprise. Most of them appear to be pictures of the crowd, rather than of the Sun… and, as with any google search, some appear to be unrelated.
Yes, but it’s also evidence for any number of other, more likely events: that my friends are pulling a prank, that they are mistaken, that a prank has been pulled on them, etc. etc.
That is true.
We don’t need to enumerate them all; what’s important here is only the posterior probability. If it is minute, then the reasonable course of action is to say, “until I see that shark, I won’t believe that you guys caught it, sorry”. There’s a huge difference between saying that, and saying, “even though the chances that you caught that shark are even smaller than the chances of a meteorite hitting me in the head anytime soon, I can’t come up with a better explanation off the top of my head so I’ll believe you, good job !”
But the posterior probability doesn’t just depend on the evidence; it also depends on the prior probability. The prior probability assigned to the shark being caught is substantially lower than the prior probability I’d assigned to the existence of God. The analogy breaks down at the selection of priors.
And the problem with the proposition G, which means “a god of some kind exists”, is that it’s starting to look like for any piece of evidence E, P(G|E) is lower than P(x|E), where x is pretty much any other non-divine explanation; and there is a lot of other evidence that can raise P(x).
I suspect that this is a rather severe exaggeration. I can easily propose an infinite number of proposals for ‘x’ where ‘x’ is non-divine but where P(G|E)>P(x|E) for almost any E. My method for finding these proposals for ‘x’ would be to string together a number of randomly selected grammatically correct sentence starting with the word ‘because’; this would result in a number of entirely nonsensical proposals. Similarly, I can randomly select evidences E, placing them before the ‘because’.
I shall assume you meant, therefore, that “there exists at least one non-divine explanation ‘x’ for which P(x|E)>P(G|E) for any given evidence E”.
So, is there any piece of evidence E for which P(G|E) is much higher than any alternatives ? Moses, presumably, got exactly such a piece of evidence in the form of a burning bush.
You’ve at least partially answered your own question; Moses saw the evidence in the burning bush. One particular monk saw the evidence in the Miracle of Lanciano. Several thousand people saw the evidence in the Miracle of the Sun. Doubting Thomas saw the evidence in the resurrected Jesus.
Lots of people saw evidence in first-hand observation of miracles.
We don’t have that, however; what we’ve got is an ancient story about a guy who saw a burning bush, and experience tells us that ancient stories mostly can’t be trusted—or else we’d be forced to believe in Zeus, Shivah, the Jade Emperor, etc., possibly at the same time.
That’s the trouble; as soon as you get to second-hand observation, the evidence is a whole lot less convincing. If you’ve set the prior for God’s existence sufficiently low, then there isn’t going to be enough second-hand evidence to alter that.
As you have anticipated, I am unconvinced by your report, but the question is, why are you convinced ? You say:
So, what makes me trust the evidence? I remember it; and I do not believe there was any way that any human could have faked that experience.
But these aren’t the only possibilities. Even if you cannot come up with any others (such as a random brain malfunction, as Jiro points out), why is this experience sufficient to convince you that a miracle occurred—given that, as you agreed above, the probability of such an event is minute ? Don’t you want to see the actual shark, before making your conclusions ?
Because I did see the shark, to extend the metaphor. And then it swam away, on its own business.
There appear to have been quite a few pictures—somewhat to my surprise. Most of them appear to be pictures of the crowd, rather than of the Sun...
Are there any photos (or preferably videos) of the event itself ? I’m looking for something along the lines of this—although, admittedly, volcano eruptions are relatively mundane events by comparison.
The prior probability assigned to the shark being caught is substantially lower than the prior probability I’d assigned to the existence of God.
Ah, I see, that is interesting. What is the ballpark prior probability you place on the existence of God (or any other god, for that matter) ?
I shall assume you meant, therefore, that “there exists at least one non-divine explanation ‘x’ for which P(x|E)>P(G|E) for any given evidence E”.
Yes, good call.
Lots of people saw evidence in first-hand observation of miracles.
It would be more accurate to say something like, “we have a lot of historical texts that describe people who claim to have seen miracles”. The distinction is important, because we have a veritable deluge of such texts regarding all major religions, as well as more modern phenomena such as alien abductions, Bigfoot, etc. The problem with such second- and third-hand accounts are that they—as you have pointed out—are notoriously unreliable.
I do not believe that little gray aliens have ever visited Earth, despite the claims of many, many “abductees”. Do you ? If not, why not, and what would it take to convince you ? You say:
Because I did see the shark, to extend the metaphor. And then it swam away, on its own business.
So, to recap: if someone told you about this shark, you would not believe him. Similarly, you do not believe that your shark story is convincing enough to convert another rational person to your belief. I think we are in agreement on these two points.
One thing I don’t understand, though, is why are you convinced ? Do you believe yourself to be that much better—orders of magnitude better—at detecting the presence of sharks (or gods) than any other person ? If so, then for what reason ? But if not, then why are you privileging your own perceptions, given that they are no better than anyone else’s ?
Think of all the alternative explanations you’d come up with if I told you, “guess what, I was abducted by little gray men from space yesterday”. Do not these explanations also apply to yourself ?
Are there any photos (or preferably videos) of the event itself ? I’m looking for something along the lines of this—although, admittedly, volcano eruptions are relatively mundane events by comparison.
There won’t be videos; the event in question happened in 1917, and the earliest video cameras were apparently first used in the 1930s. And I’m not sure that anyone can get a halfway reasonable photo of a very bright light source using 1917 camera technology—which doesn’t mean that no-one did, of course.
But if it doesn’t turn up in a Google search, then I have no idea where else to look for such a picture; should one even exist.
The prior probability assigned to the shark being caught is substantially lower than the prior probability I’d assigned to the existence of God.
Ah, I see, that is interesting. What is the ballpark prior probability you place on the existence of God (or any other god, for that matter) ?
To the existence of an omniscient, omnipotent being, I’d assigned a prior probability of somewhere over 50%.
It would be more accurate to say something like, “we have a lot of historical texts that describe people who claim to have seen miracles”
An excellent point. Very well, then; lots of people claim to have seen evidence in first-hand observation of miracles.
I do not believe that little gray aliens have ever visited Earth, despite the claims of many, many “abductees”. Do you ? If not, why not, and what would it take to convince you ?
I consider the prior probability that little gray aliens have ever visited Earth to be very small. Despite this, they have become sufficiently mimetic in modern culture that I would consider them a prime choice for hoaxsters; this, in turn, results in me sharply discounting second-hand accounts.
To convince me that aliens have visited Earth will require some piece of physical evidence; perhaps either something made from a material that can be proven not to have come from this planet (and considering what we can make, that might be a tough order) or some piece of technology not merely unavailable to humanity but significantly distant from what is available. I would not necessarily need to hold the evidence in my own hands; I would merely need to be convinced that said evidence exists (e.g. through news reports from reliable sources - ‘Scientists Study Alien Technology’).
So, to recap: if someone told you about this shark, you would not believe him.
This depends on my prior. For the existence of God, my prior is high enough that I would consider it plausible that he is telling the truth. For finding an actual shark in a lake fed and drained by small streams, my prior is far, far lower.
Similarly, you do not believe that your shark story is convincing enough to convert another rational person to your belief.
Yes, this is correct.
One thing I don’t understand, though, is why are you convinced ?
Largely because I started with a very high prior. My very high prior was contingent on the word of my parents, and particularly of my father, a wise and intelligent man who is far better than me at telling true from false. He’s not infallible, but if he says something is certainly true, then I consider that a good reason to set a high prior for that datum (before updating on any other available evidence, of course).
Think of all the alternative explanations you’d come up with if I told you, “guess what, I was abducted by little gray men from space yesterday”. Do not these explanations also apply to yourself ?
Many of them do not. I know that I am not making up the story. I know that I am not lying. I know that I was not dreaming. I know that I had not received any major head injuries at around the same time. That covers the majority of the probability with regard to reasons why you might claim to have been abducted by little gray aliens.
As a first-hand observer, I can discount all of those explanations.
Also, my prior for the existence of little gray men from space is fairly low; which would lead to me assigning extra probability to the various ‘lying’ categories.
Right, but there were no records of the event itself, just records of people’s testimonies. This is somewhat… odd. When e.g. a volcano erupts there is usually tons of footage of the actual event. People can be mistaken, or they can lie; but it’s hard to argue with a giant flaming mountain.
Yes, but it’s also evidence for any number of other, more likely events: that my friends are pulling a prank, that they are mistaken, that a prank has been pulled on them, etc. etc. We don’t need to enumerate them all; what’s important here is only the posterior probability. If it is minute, then the reasonable course of action is to say, “until I see that shark, I won’t believe that you guys caught it, sorry”. There’s a huge difference between saying that, and saying, “even though the chances that you caught that shark are even smaller than the chances of a meteorite hitting me in the head anytime soon, I can’t come up with a better explanation off the top of my head so I’ll believe you, good job !”.
You said,
But beliefs do not exist in a vacuum. Instead, they form a Bayesian network: pieces of evidence affect the posterior probabilities of some beliefs; those beliefs change the prior probabilities of other beliefs, and so on. And the problem with the proposition G, which means “a god of some kind exists”, is that it’s starting to look like for any piece of evidence E, P(G|E) is lower than P(x|E), where x is pretty much any other non-divine explanation; and there is a lot of other evidence that can raise P(x). This is what I was driving at earlier with my hypothetical Alpha-god.
So, is there any piece of evidence E for which P(G|E) is much higher than any alternatives ? Moses, presumably, got exactly such a piece of evidence in the form of a burning bush. We don’t have that, however; what we’ve got is an ancient story about a guy who saw a burning bush, and experience tells us that ancient stories mostly can’t be trusted—or else we’d be forced to believe in Zeus, Shivah, the Jade Emperor, etc., possibly at the same time.
As you have anticipated, I am unconvinced by your report, but the question is, why are you convinced ? You say:
But these aren’t the only possibilities. Even if you cannot come up with any others (such as a random brain malfunction, as Jiro points out), why is this experience sufficient to convince you that a miracle occurred—given that, as you agreed above, the probability of such an event is minute ? Don’t you want to see the actual shark, before making your conclusions ?
There appear to have been quite a few pictures—somewhat to my surprise. Most of them appear to be pictures of the crowd, rather than of the Sun… and, as with any google search, some appear to be unrelated.
That is true.
But the posterior probability doesn’t just depend on the evidence; it also depends on the prior probability. The prior probability assigned to the shark being caught is substantially lower than the prior probability I’d assigned to the existence of God. The analogy breaks down at the selection of priors.
I suspect that this is a rather severe exaggeration. I can easily propose an infinite number of proposals for ‘x’ where ‘x’ is non-divine but where P(G|E)>P(x|E) for almost any E. My method for finding these proposals for ‘x’ would be to string together a number of randomly selected grammatically correct sentence starting with the word ‘because’; this would result in a number of entirely nonsensical proposals. Similarly, I can randomly select evidences E, placing them before the ‘because’.
I shall assume you meant, therefore, that “there exists at least one non-divine explanation ‘x’ for which P(x|E)>P(G|E) for any given evidence E”.
You’ve at least partially answered your own question; Moses saw the evidence in the burning bush. One particular monk saw the evidence in the Miracle of Lanciano. Several thousand people saw the evidence in the Miracle of the Sun. Doubting Thomas saw the evidence in the resurrected Jesus.
Lots of people saw evidence in first-hand observation of miracles.
That’s the trouble; as soon as you get to second-hand observation, the evidence is a whole lot less convincing. If you’ve set the prior for God’s existence sufficiently low, then there isn’t going to be enough second-hand evidence to alter that.
Because I did see the shark, to extend the metaphor. And then it swam away, on its own business.
Are there any photos (or preferably videos) of the event itself ? I’m looking for something along the lines of this—although, admittedly, volcano eruptions are relatively mundane events by comparison.
Ah, I see, that is interesting. What is the ballpark prior probability you place on the existence of God (or any other god, for that matter) ?
Yes, good call.
It would be more accurate to say something like, “we have a lot of historical texts that describe people who claim to have seen miracles”. The distinction is important, because we have a veritable deluge of such texts regarding all major religions, as well as more modern phenomena such as alien abductions, Bigfoot, etc. The problem with such second- and third-hand accounts are that they—as you have pointed out—are notoriously unreliable.
I do not believe that little gray aliens have ever visited Earth, despite the claims of many, many “abductees”. Do you ? If not, why not, and what would it take to convince you ? You say:
So, to recap: if someone told you about this shark, you would not believe him. Similarly, you do not believe that your shark story is convincing enough to convert another rational person to your belief. I think we are in agreement on these two points.
One thing I don’t understand, though, is why are you convinced ? Do you believe yourself to be that much better—orders of magnitude better—at detecting the presence of sharks (or gods) than any other person ? If so, then for what reason ? But if not, then why are you privileging your own perceptions, given that they are no better than anyone else’s ?
Think of all the alternative explanations you’d come up with if I told you, “guess what, I was abducted by little gray men from space yesterday”. Do not these explanations also apply to yourself ?
There won’t be videos; the event in question happened in 1917, and the earliest video cameras were apparently first used in the 1930s. And I’m not sure that anyone can get a halfway reasonable photo of a very bright light source using 1917 camera technology—which doesn’t mean that no-one did, of course.
But if it doesn’t turn up in a Google search, then I have no idea where else to look for such a picture; should one even exist.
To the existence of an omniscient, omnipotent being, I’d assigned a prior probability of somewhere over 50%.
An excellent point. Very well, then; lots of people claim to have seen evidence in first-hand observation of miracles.
I consider the prior probability that little gray aliens have ever visited Earth to be very small. Despite this, they have become sufficiently mimetic in modern culture that I would consider them a prime choice for hoaxsters; this, in turn, results in me sharply discounting second-hand accounts.
To convince me that aliens have visited Earth will require some piece of physical evidence; perhaps either something made from a material that can be proven not to have come from this planet (and considering what we can make, that might be a tough order) or some piece of technology not merely unavailable to humanity but significantly distant from what is available. I would not necessarily need to hold the evidence in my own hands; I would merely need to be convinced that said evidence exists (e.g. through news reports from reliable sources - ‘Scientists Study Alien Technology’).
This depends on my prior. For the existence of God, my prior is high enough that I would consider it plausible that he is telling the truth. For finding an actual shark in a lake fed and drained by small streams, my prior is far, far lower.
Yes, this is correct.
Largely because I started with a very high prior. My very high prior was contingent on the word of my parents, and particularly of my father, a wise and intelligent man who is far better than me at telling true from false. He’s not infallible, but if he says something is certainly true, then I consider that a good reason to set a high prior for that datum (before updating on any other available evidence, of course).
Many of them do not. I know that I am not making up the story. I know that I am not lying. I know that I was not dreaming. I know that I had not received any major head injuries at around the same time. That covers the majority of the probability with regard to reasons why you might claim to have been abducted by little gray aliens.
As a first-hand observer, I can discount all of those explanations.
Also, my prior for the existence of little gray men from space is fairly low; which would lead to me assigning extra probability to the various ‘lying’ categories.